The Indian Academy

Nehrugram DEHRADUN

Question Bank – 2013-14

Subject - MATHS

Class - IX

1 Mark Questions

(Algebra)

1. What type of geometrical figure is formed by the lines x = -3, y=2, x=3, y=-2

2. Ten years ago, a father was 10 times as old as his son. Find a linear eqn expressing their

present age.

3. Find the eqn of a line parallel to x-axis and 4 units above the origin.

4. What is the condition that the eqn

ax+by+c = o represents a linear

eq

n in two variables.

5. The graph of straight line y = m is parallel to which axis.

6. Name the geometrical figure formed by the straight lines x=4, y=-4, x = -4, y = 4

7. What kind of solution does linear eqn 5x-3y=7 has ?

8. If (2,0) is a solution of the linear eqn 2x + 3y = K, then find the value of K.

9. How many linear eqns in x and y can be satisfied by x=3 and y=2 ?

10. Find the eqn of straight line, whose graph passes through the origin.

11. The graph of linear eqn X= -2 is parallel to ……………

12. A point is on y-axis and 2 units above the origin find its co-ordinate.

13. If x=2 +1 and y= , is a solution of the equation 2x-3y + 5=0 find the value of .

14. If x=1 and y=6 is a solution of the equation 8x-ay+a2= 0 find the value of a.

15. Write the eqn representing x-axis.

16. Write the eqn of a line passing through (0,4) and parallel to x-axis.

17. Write the eqn of a line parallel to y-axis and passing through the point (-3,-7)

18. The cost of ball pen is `5 less than half of the cost of fountain pen. Write statement as a

linear eqn in two variables.

19. Equation of the line on which the point (0,-6) …………… 20. The cost of petrol in a city is Rs.40 per liter write an eq

n with x as number of litres and y

total cost.

21. P and Q are two points lying on sides DC and AD respectively of parallelogram ABCD.

Then find ratio ar (APB) : ar (BQC)

22. In the figure ABCD is a parallelogram, then

P

Find

A B

D C

23. If a rectangle and a square stand on the same base and between the same parallels, then

the ratio of their area is ………………

24. If a triangle and a parallelogram are on the same base and between the same parallels,

then the ration of the area of the triangle to the area of parallelogram is …………..

25. If area of parallelogram ABCD = 25 cm2 and on the same base CD a ∆BCD is given such

that ar (∆BCD) = x, then find value of x.

26. In the given figure, ABCD is a parallelogram if <A=650 then (<B+<D) is equal to

………..

D C

A 650 B

27. A quadrilateral, whose diagonals bisect at right angles, is called ……………….

28. In a quadrilateral ABCD, AB=BC and CD=DA then what type of quadrilateral ABCD

is ?

29. In the adjoining fig, if DE // BC, then find BD

A

6cm 3cm

D E

3cm

B C

30. The figure obtained by joining the mid points of the sides of a rhombus, taken in order is

………………

31. In ∆ABC, AD is median of a ∆ABC and BE is median of ∆ABD. If ar (∆ABE) = 15cm2

then find ar (∆ABC)

A

E

B D C

32. Find x in the adjoining fig. O is the centre of the circle.

A

50o

x

O

B C

33. In the below PQRS is cyclic quadrilateral. If <SPR =250 and <PRS =60

0, then find value

of X. R

S Q

60O x

25o

P

34. <ADB = 900 and <ABC=30

0 then find <CA0

C O

D

A B

35. In the given fig ‘O’ is the centre of the circle <ABO = 200 and <ACO = 30

o where A,B,C

are points on the circle. Find the value of x

A

0

200 30

0

x

B C

36. In fig , O is the centre of the circles and <ABC =400 then find <AOC

B

O 400

A C

37. In the fig In the fig AB is a diameter. <BDC=350, then find <ABC

C

B

A

D

38. If ABC is an arc of a circle and < ABC = 600 then the ratio of arc to the circumference is

…………………

39. Number of circles passing through three non-collinear points is ……….

MENSURATION

40. Curved surface area of a hemisphere with radius 7 cm is……………..

41. If the total surface area of a cube is 54cm2 then its lateral surface area is ……………..

42. If in a right circular cylinder, radius is doubles and height is halved, then the curved

surface area will be …………..

43. The total surface area of solid hemisphere is 462 cm2

. Find its diameter.

44. In a cylinder, if radius is halved and height is double, the curved surface area will be

……………

45. The radius of a sphere is numerically equal to its surface area then find its diameter.

46. Find curved surface area of a right circular cone whose slant height is 10cm and base

diameter is 14cm.

47. The total surface area of an open cuboidal box of dimensions l x b x h is ……….

48. Curved surface area of hemisphere of diameter 2r is ………..

49. If volume and surface area of a cylinder are numerically equal, then radius of its base is

…….

50. If the radius of a sphere is doubled, then its volume is increased by how much percent.

51. The total surface area of a cube is 96 cm2 then find its volume.

52. If the heights of two cones are in the ratio 1:4and the radius of their bases are in the ratio

4:1 then find the ratio of their volumes.

53. Find the total surface area of a cone whose radius is

and slant height is 2l.

54. If the diameter of a solid cone of radius r is the same as its height, then find the volume of

the cone.

55. If the area of a base of right circular cylinder is 54cm2 and its height is 10cm then find its

volume

56. In a cylinder, if radius is halved and height is doubled then its volume will be ………….

57. Find the volume of cone of radius

and height 2h.

58. If radius of a sphere is

then its volume is ……………

Or

A match box measures 6cm x 2cm x 1.5 cm, then find volume of a packet containing five

such boxes.

Or

If A,B, and C denote the areas of three adjacent faces of a cuboid, then find its volume.

(Statistics and Probability)

59. Class mark of a class interval 15-25 is …….

60. The ages (in year) of 10 children are given below:

15,15,16,16,15,14,17,16,14,16. The modal age of the children is …………………

61. The mean of x+1. x+3,x+4,x+8 is ………..

62. Find the mean of first 10 natural numbers.

63. The mean of first 5 prime numbers is …………….

64. Median of 78,56,22,34,45,54,39,84,54 is ………………

65. Median of 12,11,7,6,10,17,9,15,13, is ……..

66. Find the mode of the following marks obtained by 20 students :

4,6,5,9,3,9,7,7,6,5,4,9,10,10,3,4,7,6,9,9

67. The relation between mean, median and mode is …………..

68. For what value of x, is the mode of the following data 17,

15,16,17,14,17,16,13,x,17,16,15,15

69. In the throw of a die in a game of snakes and ladder, what is the probability of getting an

even number.

70. A Coin is tossed 10 times with the frequencies head =4, tail =6, the probability of no head

is ………..

71. Reena dialed a phone number 100 times in a week out of which she gets the response 55

times. Find the probability that she will not get the response.

72. An experiment has two outcomes E and F then P (E) + P(F) is equal to …………….

73. What is the range of probability of an event given by P(E)

74. Out of 35 students participating in a debate 10 are girls. Find the probability that winner

is a boy.

75. A dice is thrown once, a number is noted, then what is the probability that it is a prime.

76. In year 2009, during rainy season of 90 days it was observed that it rained 20 days only.

Then what is the probability that it did not rain.

77. The minimum probability of an event is ………..

78. One card is drawn from a well shuffled deck of 52 cards. Find the probability that the

card drawn is an ace.

Or

A card is drawn from a well shuffled pack of 52 cards. Find the probality that the card

drawn is red card.

Or

A bag contains 6 blue and 4 green marbles. If a marble is drawn at random from the bag,

find the probability that the marble drawn is green.

Or

Two coins are tossed simultaneously 1000 times and we get.

Two heads :200 times, one head : 600 times,

No head : 200 times

Find the probability of getting at most one head.

[ 2 Mark Questions ]

79. Find the coordinates of the point where the line y=5x+7 cuts the y-axis

80. The taxi fare in a town is Rs.10 for the first kilometer and Rs. 6 per Km for the

subsequent distance taking the distance as ‘x’ km and total fare as y write a linear

equation for this information, what will be the total fare for 15 km?

81. Draw the graph of x+2y=6 and from the graph ,find the value of x when y= -6

82. Give the equation of two lines passing through (2,14). How many more such lines are

there and why?

83. If the points A (3,) and B (1,4) lie on the graph of the line ax+by=7 find the values of a

and b

[ Quadrilateral & Area]

84. Two opposite angles of a parallelogram are (3x-2) and (50-x). Find the measure of each

angle of the parallelogram.

85. Diagonals AC and BD of a trapezium ABCD with AB//DC interest each other at O.

Prove that ar ( ∆AOD) = ar (∆BOC)

86. In fig. ABC is a triangle. E is the mid-point of median AD. Show that ar(BED)=ar

(ABC)/4

A

E

B D C

87. In fig. AP//BQ//CR Prove that ar(AQC)=ar(PBR)

A P

B Q

C R

88. Show that median divides a triangle into two triangles of equal areas.

89. In figure, ABDE and BCDE are two parallelogram show that ar(∆BDE) =

ar (quad

ACDE)

E D

A B C

90. The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the

quadrilateral

91. Prove that the sum of the four angles of a quadrilateral is 3600.

92. In the given figure, E is any point on median AD of a ∆ABC. Show that ar (ABE) = ar

(ACE)

A

E

B D C

93. Show that each angle of a rectangle is a right angle.

94. If diagonals of a parallelogram are equal, show that it is a rectangle.

95. In the given figure, ABCD is a trapezium in which <A=(x+25)0,<B=y, <C=95

0 and

<D=2x+50, then find the values of x and y

C D

950 2x+5

Y x+25

B A

96. If one angle of a // gm is 240

less than twice the smallest angle, find all angles of the //

gm

97. Two adjacent angles of a //gm are in the ratio 5:4. Find all angles of the parallelogram.

100 In the given figure, ABCD is a parallelogram, AE1DC and CF1 AD. If AB=16 cm,

AE=8cm and CF=10cm, find AD.

A B

F

D E C

(Circles)

101In figure, a circle with centre O is drawn and <BAC=500,

Find x

A

O

x

B C

102 In the fig : <AOC=1100. Find <CBD where AB is produced to D

0

C

A

B

D

103 Draw a line segment AB=6Cm and draw its perpendicular bisector.

104 A Chord of a circle is equal to its radius find the angle

105 Prove that equal chords subtend equal angles at the centre.

106 Find the length of the chord which is at a distance of 3 cm from the centre of a circle

whose radius is 5 cm.

107 Prove that if chords of congruent circles subtend equal angles at their centers, then the

chords are equal.

108 If O is the centre of the circle and <BAC=1300, then find x

A

1300

B C

x

o

109 In the figure points A,B,C lie on a circle with centre O If <AOC = 1400 and <OAB=50

0

Find <OCB

C

O 1400

B

500

A

110 In figure, if <ADC = 1280 and <DBC = 32

0 find <DCB

Or

PQRS is a cycle quadrilateral, in which <p=2x0 <Q=y

0,<R=3x

0. and <2y

0, Find the values

of x and y.

111 Find the volume of the largest right circular cone that can be placed in a cube of edge 14

cm.

112 The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of

7m. Find the area available to the motorcycle for riding.

113 Two cylindrical cans have bases of the same size. The diameter of each is 14 cm. One of

cans is 10cm high and other is 20 cm high. Find the ratio of their volumes

114 Three cubes each of column 125 Cm3 are joined end to end to form a cuboid. Find the

total surface area of cuboid.

115 Find the total surface area of a hemisphere of radius 3.5cm (Take

)

116 The circumference of the edge of a hemispherical bowl is 132 Cm. Find the capacity of

the bowl.

117 Find the capacity in litres of a conical vessel whose base diameter is 14 cm and slant

height is 25 cm.

118 Find the cost of digging a cuboidal pit 8m long, 6m broad, and 3m deep at the rate of Rs. 30 per m

3.

119 Each side of a cube is increased by 50% by what percent the surface area of the cube

increases?

120 Find the cost of while washing the four walls of a room with dimensions 5mx4mx3m at

the rate ofRs.12/m2

[ STATISTICS ]

121 The class – marks of classes in a distribution are 6,10,14,18,22,26,30. Find

(a) Class size

(b) Lower limit of second class

(c ) Upper limit of last class

(d) Third class

122 Prepare a frequency distribution table for the data given below :

0,1,3,1,3,0,2,1,0,2,1,1,1,2,1,2,2,2,3,0,3,1,1,2,3,2,2,0,1,0

123 Obtain the mean of the following data.

Variable (Xi) 4 6 8 10 12

Frequency (Fi) 4 8 14 11 3

124 The following observations have been arranged in ascending order. If the medium of the

data is 63, find the value of x

29,32,48,50, x, x+2,72,78,84,95

125 The class marks of a frequency distribution are 104,114,124,134,144,154,164. Find the

class size and class intervals.

126 Find the median of the following data: 2,12,32,17,26,39,42,12,18,32,15

127 If the mean of five observations is x, x+2,x +4 x+6,x+8 is 11. Find the mean of first three

observations.

128 The mean of five numbers is 27 if one number is excluded, their mean is 25, Find the

excluded number.

129 Find the median of the data 15,28,72,56,44,32,31,43 and 51. If 32 is replaced by 23. Find

the new median.

130 The median of a data arranged in ascending order 9,14,15,20, x+1, x+3, 31,36,44,51 is

25. Find the value of 3x+3

(Probability)

131 A die is rolled 300 times and following outcomes are recorded:

Outcome 1 2 3 4 5 6

Fre. 42 60 55 53 60 30

Find the probability of getting a number more than 4.

132 To know the opinion of the students about a subject survey of 200 students was

conducted. The data is recorded as follows.

Opinion Number of students

Like 135

Dislike 65

Find the probability that a student chosen at random i. likes the subject ii. Does not like it.

133 A bag contains 5 red 8 white, 4 green and 7 black balls. If one ball is drawn at random,

find the probability that is (i) black (ii) not green

134 A coin is tossed 600 times. The outcomes are number of heads = 248, number of tails =

352. It is tossed once more find the probability of getting.

(i) A Tail (ii) A Head

135 Three coins are tossed simultaneously 200 times with the following frequencies of

different outcomes

Out come 3 Heads 2 Heads 1 Head No Head

Frequency 23 72 77 28

I f the the three coins are simultaneously tossed again ,compute the probability of more

than two heads.

136 In a cricket match 1 batswoman hits the boundary 16 times out of 40 balls she plays. Find

the probability of her not hitting the boundary.

137 The percentage of marks obtained by a student in the monthly unit are given below –

Unit test I II III IV V

% of marks obtained 76 52 60 95 43

138 A man speaks truth 4 out of 7 times. Find the probability of that he would narrate an

incident

(i) Correctly (ii) Incorrectly

139 There are 10 balls in a bucket numbered 1,1,2,3,4,4,4,5,6.6 A Single ball is randomly

picked. Find the probability of

(i) Drawing a ball numbered 4

(ii) A ball with number less than 4

140 1000 families with 2 children were selected randomly and the following data were

recorded

Number of boys in family 0 1 2

Number of families 140 560 300

If a family is chosen at random. Find the probability

(i) No boy (ii) at least one boy

[ 3 Mark Questions ]

141 Mark two points A (-2,0), B(2,0) in the Cartesian plane graph. Name the equation passing

through A and B. Does origin lies on this line?

142 Solve the equation 3x+5 = 2x+3 and represent the solution on the number line and

Cartesian plane.

143 Compare the equation

+

y + 4 = 2y-3 and lx + my –n=o and write the value of l,m

and n

144 By means of graph, verify that x=2, y=2, is a solution of the equation 2x-y=2

145 Express the following statement as a linear eqn in two variables by taking present ages (in

years) of father and son as x and y respectively. Age of father 5 years ago was two years

more than 7 times the age his son at that time.

146 Find two linear equations in two variables whose graphs pass through (2,14). How many

such equations are possible?

147 Given a point (2,3) form an equation of a line on which it lies. How many such equations

are possible?

148 For what value of a and b, the points (2,3) and (4,0) lie on the graph of the equation

ax+by = 7 ?

149 If the point (3,5) lies on the graph of eqn 2y=px-2, find p. Also find two more solutions

for the given equation.

150 Find the value of K, if x=2, y=1 is a solution of the equation 2x +3y = K. Hence find two

more solutions of the equation.

151 Draw the graphs of y=x and y=-x in the same axes. Also, find the coordinates of the point

where the two lines intersect.

152 Draw the graph of the linear equation y=

x +

. Check from the graph that (7,5)is a

solution of the linear equation.

153 Draw the graph of y=3 as an equation in two variables what does the graph represent?

154 Write the equation 2x=y in the form ax+by+c=0 and find values of a,b,c in the equation.

How many solutions this equation has?

155 Using graph, verify that point (2,6) lies on the graph of 3x-2y+6 = 0

156 Draw the graph of 3x+2y-1 = 0. Check from the graph whether the points (1,-1) and (-

1,1) lie on the graph or not.

157 Find the coordinates of the points where the line representing the equation

=1-

cuts

the x-axis and the y-axis.

158 If (3,1) is a solution of the equation 3x-2y=k, find the value of K. Find two more solution

for the equation.

159 Express y in terms of x in the equation 2x-3y=12. Draw the graph of the above linear

equation. Find the point where the line cuts x-axis and y-axis.

160 The auto fares in a city are as follows. For the first Km, the fare is Rs.12 and the

subsequent distance is Rs 7 per Km.Taking the distance covered as x Km and the total

fare as Rs.y, write a linear equation and draw its graph

(Quadrilateral & Area)

161 In the given figure, PQRS and ABRS are //gms and x is any point on side BR.

Show that -

(i) ar(PQRS) = ar (ABRS)

(ii) ar (AXS) =

ar (PQRS)

P A Q B

X

S R

162 The diagonals of a parallelogram divide it into two congruent triangles. Prove.

163 E is the mid – point of the side AD of a trapezium ABCD with AB//DC . A line through

E drawn parallel to AB intersects BC at F. Show that F is the mid-point of BC.

164 ABCD is a quadrilateral in which P,Q, R and S are mid-points of the sides AB,BC,CD

and DA respectively. Show that PQRS is a parallelogram.

165 If a line is drawn parallel to the base of an isosceles triangle to interest its equal sides,

Prove that the quadrilateral so formed is cyclic.

166 In the figure, ABCD is a parallelogram. E and F are the mid- points of sides AB and CD

respectively show that the line segments AF and EC trisect the diagonal BD.

D F C

P

Q

A E B

167 In the figure BD = DE = EC

Prove that ar(∆ABD) =

ar (∆ADC)

A

B D E C

168 If the diagonals of a //gm are equal and intersect at right angles, then show that //gm is a

square.

169 Prove that the line segment joining the mid-points of the hypotenuse of a right triangle to

its opposite vertex is half of the hypotenuse.

170 ABCD is a quadrilateral such that AB=CD, diagonals AC and BD intersect at O. Such

that OA=OC. AL and CM are perpendiculars drawn from A and C on BD. Show that (a)

ar (∆OAB) = ar (∆OCD)

171 Diagonals AC of Parallelogram ABCD bisects <A show that:

(i) It bisects <C also.

(ii) ABCD is a rhombus

172 If the non-parallel sides of trapezium are equal, prove that sum of each pair of opposite

angles is supplementary.

173 P is a point in the interior of a parallelogram ABCD. Show that ar(APB) + ar(PCD) =

ar

(ABCD)

174 Prove that the diagonals of a parallelogram bisect each other.

175 In quadrilateral ABCD, <B=900, <C-<D=60

0 and <A-<C-<D=10

0. Find <A,<C and <D

176 Show that the diagonals of a rhombus are perpendicular to each other.

177 E and F are points on the diagonal AC of a parallelogram ABCD such that AE=CF. Show

that DFBE is a parallelogram.

D C

F

E

A B

178 In a parallelogram ABCD, prove that sum of any two consecutive angles is 1800.

179 Prove that a parallelogram and a rectangle on the same base and between the same

parallels are equal in area.

180 In the figure ABCD is a trapezium in which side AB is parallel to side DC and E is the

mid-point of side AD. If F is a point on the side BC such that the seGment EF is parallel

to side DC. Prove that F is the mid-point of BC and EF =

(AB+DC)

A B

E G F

D C

[Surface Area and Volume]

181 What length of canvas 3m wide will be required to make a conical tent of height 8m and

radius of base 6m ? (use π = 3.14)

area decreased.

183 How many spherical bullet can be made out of a solid cube of lead, whose edge measures

44 cm, each bullet being 4 cm in diameter.

184 A Sphere and a cube have the same surface area show that the ratio of the colume of the

sphere to that of the cube is : √ : √

185 The radius of a spherical ballon increases from 7 cm to 14 cm as air being pumped into it.

Find the ratio of surface areas of the balloon in two cases.

186 A hemispherical bowl is 0.25 Cm thick. The inner radius of bowl is 5 Cm, find the outer

curved surface area and volume of the bowl (keep volume in )

187 How many litres of milk can be put in six hemispherical bowls each of radius 35 Cm.

188 A hemispherical dome of a building needs to be painted. If the circumference of the base

of the dome is 17.6m, find the cost of painting it, if the cost of painting is Rs.5 per 100

cm2 [Take π =

]

189 The internal and external diameter of a hollow hemisphere vessel are 24cm and 25 cm

respectively. The cost to paint 1 sq cm of surface isRs. 1.75. Find the total cost to the

nearest rupee to paint the vessel all over. Ignore the area of the edge ( Take

190 A rectangular piece of paper is 22 cm long and 12 cm wide. A cylinder is formed by

rolling the paper along its length. Find the volume of the cylinder. ( =

)

191 A hollow cylindrical pipe is 210 cm long. Its outer and inner diameter are 10 cm and 6

cm respectively. Find the volume of the copper used in making the pipe.

192 Find the volume of a sphere whose surface area is 55.44 cm2 ( =

)

193 The radius and vertical height of a cone are 5 cm and 12 cm respectively. Find the curved

surface area.

194 A cube of largest volume is cut from a sphere of radius 4 √ . Find the volume of the

cube ( =

)

195 A right triangle PQR with sides 3 cm,4cm and 5cm is revolved about the side of length 4

cm. Find the volume of the shape so generated ( use = 3.14 )

196 The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How

many bricks of dimensions 22.5 cm x 10cm x 7.5 cm can be pained out of this container?

197 The slant height and base diameter of a conical tomb are 25 m and 14m respectively.

Find the cost of white washing its curved surface at the rate of Rs.210 per 100 m2.

Use ( =

)

198 A short put is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.5g per

cm3, find the mass of the short-put.

199 Radhika has the frame of a lampshade in the form of a cylinder. The frame has a base

diameter of 20 cm and height of 30cm. She wants to cover it with a decorative cloth. A

margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find

how much cloth is required for covering the lampshade.

200 A village having a population of 2000 required 150 liters of water per head per day. It has

a tank measuring 20m x15m x 6m. For how many days will be water of this tank last?

(Constructions)

201 Construct an angle of 150using scale and compass only.

202 Construct angle 750 using ruler and compass only.

203 Draw a triangle ABC in which BC=4cm, AB=3cm and <B=37.50

204 Construct an angle of 1050, using ruler and compass only.

205 Construct an angle of 450 using compass and ruler only.

206 Construct a ∆PQR with base PQ=4.2 cm <P=450 and PR-QR = 1.4cm

207 Construct a ∆ABC with BC=5.5cm, <B=600 AB+AC = 8cm.

208 Construct a triangle ABC with base AB=5cm, <A=300 and AC-BC=2.5 Cm

209 Construct a ∆ABC, in which BC=3.8cm, <B=450 and AB+AC=6.8cm.

210 Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is

18cm.

[Statistics]

211 Find the value of x any y in the following distribution if it is know that the mean of the

distribution is 1.46

No of accident 0 1 2 3 4 5 Total

Frequency 46 X Y 25 10 5 200

212 The mean weight of 60 students of a class is 52.75 kg. If the mean weight of 25 students

of this class is 51kg, find the mean weight of the remaining 35 students of the class.

213 Find the mean for the data

Xi 10 15 20 25 30

Fi 4 6 3 2 5

214 100 surnames were randomly picked up from a telephone directly and frequency

distribution of the number of letters in the English alphabet in the surnames was found to

be as follows –

Numbers of Letters Number of Surnames

2-4 6

4-6 30

6-8 44

8-12 16

12-14 4

Draw a histogram to depict the given information.

215 Find the missing frequency ‘K’ from the following data:

Xi 5 10 15 20 25

Fi 2 8 K 10 5

If it is given that mean is 16

216 Given below is the number of seats won by different political parties in an election.

Political party A B C D E F

Number of seats won 75 52 35 42 30 47

Draw a bar graph to represent the above data.

217 Construct a frequency polygon for the following data.

Class 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 5 10 13 9 6 2

219 If the mean of the following observations is 18 then find out the value of the disappeared

frequency P

X 10 15 20 25

F 5 10 P 8

220 Draw histogram for the following data :

Class interval 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 6 8 12 7 5 4

221 The population of four major cities in India in a particular year us given below:

City Mumbai Kolkata Delhi Chennai

No of Students 120 130 150 80

Draw bar graph

222 The time taken in seconds, to solve a problem by each of 25 pupils is as follows :

16,20,26,27,28,30,33,37,38,40,42,43,46,46,46,48,49,50,53,58,59,60,64,52,20

Construct a frequency distribution for these data, using a class interval of 10 seconds.

223 Find the value of P, if the mean of the following distribution is 20.

X 15 17 19 20+P 23

F 2 3 4 5P 6

224 Find the median of the following observations:

46,64,87,41,58,77,35,90,55,92,33. If 92 is replaced by 99 and 41 by 43 in the above data

find the new median?

225 30 children were asked about the number of hour they watched TV programs in the

previous week. The results were found as follows.

1,6,2,3,5,,12,5,8,4,8,10,3,4,12,2,8,15,1,17,6,3,2,8,5,9,6,8,7,14,12

a) Make a frequency distribution, taking class width 5

b) How many children watched TV for 15 or more hours a week.

(Probability)

226 Three coins are tossed 1000 times and the outcomes are recorded as below :

No of Heads 3 2 1 0

Frequency 200 285 312 203

Find the probability of ,two heads ,not more than one head,more than two heads

227 In a survey of 500 families, number of vehicles owned per family were found to be as

follows.

No of vehicles owned 0 1 2 3 4

No of families 35 213 170 65 17

Find the probability ,no vehicle, 2 or 3 vehicles, more than 1 vehicle

228 The weekly pocket expenses of students are given below. Find the probability that the

weekly pocket expenses of a student are.

i) Rs.59

ii) More than Rs 59

iii) Less than Rs 59

Pocket expenses

(In Rs.) 45 40 59 71 58 63 65

No of students

7 4 10 6 3 8 1

229 A die is thrown 1000 times with the following frequencies for the outcome 1,2,3,4,5, and

6 as given below :

Outcome 1 2 3 4 5 6

Frequency 175 125 250 150 100 200

Find the probability of getting 2,4 and 6

230 A die is rolled 25 times and outcomes are recorded as under

Outcomes 1 2 3 4 5 6

Frequency 9 4 5 6 1 0

It is thrown one more time find the probability of getting

a) An even number

b) A multiple of 3

c) A Prime number

231 Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card

is drawn from this box. Find the probability that the number on the card is :

a) a number less than 14

b) a number which is a perfect square

c) a prime number less than 20

232 Two coins are tossed simultaneously 500 times and following observations were noted.

Two heads

105

One Head

275

No head

120

Find the probability of occurrence of events

i) Two heads

ii) One head

iii) No head

233 The ages of workers in a factory are given in the following table :

Age (In years) 21-23 23-25 25-27 27-29 29-31 31-33 33-35

No of workers 3 4 5 6 5 4 3

Find the probability that the age of workers selected at random is at least 25 years.

234 To know the opinion of the students about mathematics, a survey of 200 students was

conducted. The data is recorded in the following table.

Opinion Like Dislike

No of students 135 65

Find the probability that a student chosen at random

i) Likes mathematics

ii) Does not like it.

235 Eleven bags of wheat flour, each marked 5 kg actually contained the following weights of

flour (in Kg) :

4.97,5.05,5.08,5.03,5.00,5.06,5.08,4.98,5.04,5.07,5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of

four.

236 In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the

probability that on a ball played:

i) he hits boundary

ii) he does not hit a boundary

237 1500 families with 2 children were selected randomly and the following data were

recorded.

No of girls in a family : 0 1 2

No of families : 211 814 475

If a family is chosen at random, compute the probability that it has :

i) At most one girl ii) 2 girls

238 The percentage of marks obtained by a student the monthly unit test are given

Unit test : I II III IV V

% of marks obtained : 58 74 76 62 85

i) At least 60% marks

ii) Marks between 70% and 80%

239 The record of a weather station shows that out of the past 250 consecutive days, its

weather forecast were correct 175 times. What is the probability that on a given day

(i) it was correct ? (ii) it was not correct?

240 In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41,39,48,52,46,62,54,40,96,52,98,40,42,52,60

Find the mean, median and mode of this data.

[4 Mark Questions]

241 Draw the graph of the equations 2x+3y=5 and x-2y=13 on the same axes. Find the

coordinates of the point where their graphs intersect each other.

242 Draw the graph of the equation 5x-4y+20=0. Find the points where the line represented

by the equation cuts x-axis and y-axis

243 If the point (4,3) lies on the graph of the linear equation 3x-ay=6, then find value of a,

also find whether (-2,6) also lies on the same graph? Draw graph of this equation.

244 For the linear equation 3x-5y-15=0, find the points where its graph intersects x and y-axis

using these draw the graph of the equation.

245 The auto rickshaw fare in a city is charged Rs.10 for the first Km and Rs.4 pr Km for

subsequent distance covered. Write the graph of this equation and find the fare for the

distance of 6m, using the graph.

246 Here is a linear equation that converts Fahrenheit temperature to Celsius temperature. F =

(

)C + 32

i) If the temp is 300C, what is the temp in Fahrenheit

ii) If the temp is 950 F, what is the temp in Celsius draw its graph also.

247 Find the value of ‘m’ If x=2,y=1 is a solution of the equation 2x+3y=m and represent it

graphically.

248 Give th geometric representation of 2x+9=0 as an equation in two variables. Give two

solutions of the equation from the graph.

249 Work done by a body on application of a constant force is directly proportional to the

distance travelled by the body. Express this in the form of an equation in two variables.

Draw the graph of the equation taking in two variables. Draw the graph of the equation in

two variables. Draw the graph of the equation taking force as 5 units. Find from the graph

the work done when the distance travelled by the body is 2 units.

250 Taxi fare in a city is Rs.8.00 for first Km and for the subsequent distance it is Rs. 5.00

per Km. Write an equation to represent this information in two variables taking distance

covered as ‘x’ Km and total fare as y (In Rs.). Find the distance travelled by a person if

he spent Rs.63.00 represent this information graphically.

251 Draw graphs of 3x-2y=1 and 2x+y= -4 and write the coordinates of the point where the

graphs intersect.

252 Give the geometric representation of 2x+8=0 as an equation

i) In one variable

ii) In two variables.

253 Solve the equation 3(x+2) = 2(2x-1) and represent the solution on

i) the number line

ii) the Cartesian plane.

254 Yamini and Fathima, two students of class IX together contributed RS.100 towards the

prime minister’s relief fund to help the earthquake victims. Write a linear equation which

satisfies this information. Draw the graph of the same by taking their contributions as `x

and `y.

255 Sketch the graph of the equation y=2x-4. Shade the region enclosed by the line and the

two axes.

256 A man is driving his car with a uniform speed of 90km/hr. Draw the time-distance graph

from the graph find the distance travelled by him in 2

Hrs.

257 Draw the graphs of line x+y =6 and 2x+3y=16 on the same graph. Also the co-ordinates

of the point where two lines intersect.

258 The monthly hostel charges for a student comprises of Rs.1000 P.M. as fixed boarding

charges and remaining charges at the rate of Rs 50 per day (for the no for which the food

has been availed by a students)

a) Form a linear eqn in two variables to represent above situation

b) What are the monthly charges to be paid by a student who availed meals for 21 days in

a given month?

259 If (2,3) and (4,0) lie on the graph of equation ax+by=1. Find value of a and b. Plot the

graph of equation obtained.

260 Draw the graph of the linear equation 3x+4y=6 At what points, the graph cuts the x-axis

and the y-axis.

261 Draw the graph of two lines, whose equations are 3x-2y+6=0 and x+2y-6=0 on the same

graph paper. Find the area of triangle formed by the two lines and x-axis.

[ Quadrilaterals and Area]

262 P,Q,R and S are mid-points of the sides AB, BC, CD and DA respectively of the

parallelogram ABCD. Show that PQRS is a parallelogram ABCD show that PQRS is a

parallelogram whose area is half of the parallelogram ABCD.

263 Prove that the quadrilateral formed by the internal angle bisectors of any quadrilateral is

cyclic.

264 The diagonals of a parallelogram ABCD intersect at a point 0. Through 0 a line is drawn

to intersect AD at P and BC at Q. show that PQ divides the parallelogram into two parts

of equal areas.

265 In the given fig AP║BQ║ CR prove that A P

i) ar(PSQ – ar(ASB) S

ii) arr(BTC) = ar (QTR) B Q

T

C R

266 In the figure, side AB of parallelogram ABCD is produced to any point P. AQ ║CP

meets CB produced at Q and PBQR is a parallelogram. Prove that ar(ABCD)=ar(PBQR)

D

A C

B

Q P

R

267 In a parallelogram PQRS, If <QRS = 2x, <PQS = 4x and <PSQ=3x, find the angles of the

parallelogram.

268 ABCD is trapezium in which AB║CD and AD=BC show that :

i) <A = <B ii)<C=<D

iii) ΔABC congruent BAD

269 D, E, F are respectively the mid points of the sides BC, CA and AB of a triangle ABC.

Show that:

i) BDEF is a parallelogram

ii) DFEC is a parallelogram

270 Show that the quadrilateral formed by joining the mid points of adjacent sides of a

rectangle is a rhombus.

271 Show that the line segments joining the mid points of the opposites sides of a

quadrilateral bisects each other.

272 ABCD is a rhombus and PQRS are the mid points of the sides AB, CD , and DA

respectively show that the quadrilateral PQRS is a rectangle.

273 ABC is a triangle; right angled at C A line trough the mid-point M of hypotenuse AB and

parallel to BC intersects AC at D. Show that

i) D is the mid – point of AC

ii) MD I AC

iii) CM=MA =

AB

274 ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on

the diagonal BD. Show that AP=CQ

275 Two parallel lines l and m are intersected by a transversal P. Show that the quadrilateral

formed by the bisectors of interior angles is a rectangle.

276 Prove that in a triangle, the line segment joining the mid-points of any two sides is

parallel to third side and is half of it.

277 P is midpoint of side BC of a parallelogram ABCD, such that <BAP=<DAP. Prove that

AD=2 CD.

278 Show that the bisectors of angles of a parallelogram form a rectangle.

279 Prove that the parallelograms on the same base and between same parallels are equal in

area.

280 In the given figure, XY is a line parallel to side BC of ∆ABC. BE║AC and CF║AB

meats XY at E and F respectively. Show that ar (ABE) = ar(ACF)

A

E x y F

B C

281 In a triangle ABC, E is the mid-point on median AD. Show that ar(BED) =

ar(ABC)

282 Prove that two triangles on the same base and between the same parallel lines are equal in

area.

283 Show that the diagonals of a parallelogram divide in into four triangles of equal area.

284 In figure, ABC is a triangle, D is the mid-point of AB, P is any point on BC. Line CQ is

drawn parallel to PD to intersect AB at Q. PQ is joined. Show that ar (∆BPQ) =

ar(∆

ABC)

A

Q

D

B P C

285 Prove that any cyclic parallelogram is a rectangle.

286 If the medians of a triangle ABC intersect at G, show that

ar(∆AGB) = ar (∆AGC) = ar(∆BGC) =

ar (∆ABC)

A

F G E

B D C

287 In the given figure, ABCD is a parallelogram in which E is the mid-point of AD. DF EB,

meeting AB produced in F and BC at L. Prove that DF = 2DL

D C

E L

A B F

288 If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD,

show that ar(EFGH) =

ar (ABCD)

D G C

H

F

A B

E

289 In the given figure, P is a point in the interior of a parallelogram ABCD, show that

Ar(∆APB) + ar (∆PCD) =

ar (gm ABCD)

A B

P

D C

290 ABCD is a quadrilateral in which P, Q, R and S are the mid – points of sides AB,BC,CD,

and DA respectively. AC is a diagonal show that

D R C

S Q

A P B

i) SR║AC and SR=

AC

ii) PQ=SR

iii) PQRS is a parallelogram

(Circles)

291 Prove that the angle subtended by an arc of the circle at the centre is double the angle

subtended by it any other point on the remaining part of the circle.

292 Prove that equal chords of a circle subtend equal angles at the centre of circle.

293 In the figure straight lines AB and CD pass through the centre O of the circles. If

<OCE=400 and <AOD=75

0 find <CDE and <OBE

D

E

A 0 B

P

C

294 In the figure BD=DC and <DBC=250 . Find the measure of <BAC.

A

B C

D

295 ABCD is a cycle quadrilateral whose diagonals intersect at a point E. If <DBC=700,

<BAC=300 find <BCD. Further, if AB=C, find , ECD.

D C

E

A B

296 In the figure, <PQR=1000, where P,Q, and R are points on circle with centre O, Find

<OPR.

Q

P R

O

297 In the figure, O is the centre of the circle. BD=OD and CDIAB. Find <CAB.

C

B

0

A D

298 Prove that the opposite angles of a cycle quadrilateral are supplementary.

299 In the given figure, PQ is the diameter of the circle with centre O. If <PQR=650,

<RPS=400 and <PQM=50

0, find <QPR, <PRS and <QPM.

S R

P o Q

M

[Constructions]

300 Construct A ∆ABC in which BC=5cm, <B=300 and AC-AB=2 cm

301 Construct a ∆PQR in which QR=6 cm, <Q=600 and PQ+PR=10cm

302 Construct a triangle ABC in which BC=8cm, <B=450 and AB-AC=3.5cm

303 Construct a ∆ABC in which BC=7.5cm, <B=450 and AB-AC=4 cm

304 Construct a triangle XYZ, in which <Y=300, <Z=90

0 and XY+YZ+ZX=11cm

305 Construct a triangle PQR in which QR=7cm, <Q=450 and PQ-PR=4cm

306 Construct a triangle ABC whose perimeter is 12cm, <B=600 and <C=45

0. Measure the

sides of the triangle.

307 Construct a right triangle where base is of length

308 Construction a ABC in which <C=450, <B=60

0 and AB+BC+AC = 18 cm

309 Construct a ABC with <A=750, <B=30

0 and AB=5.6 cm. Measure <C

[Surface Area and Volumes]

310 A storage tank is in the form of a cube. When it is full of water the volume of water is

15.625 m3. If the present depth of water is 1.5m, Find the volume of water already used

from the tank.

311 A semi – circle sheet of mental of diameter 28cm is bent to form an open conical cup.

Find the capacity of the cup.

312 The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm3. Find the

radius and height.

313 Monica has a piece of canvas whose area is 818 m2 she used it to have a conical tent

made, with a base radius of 10m. Assuming that all the stitching margins and the wastage

incurred while cutting amounts to approximately 1.6m2, find the volume of the tent that

can be made with it.

314 The volume of right circular cone is 9856 cm3. If the diameter of its base is 28 cm then

find

(i) Height of cone

(ii) Slant height of cone

(ii) Curved surface area of cone.

315 The floor of a rectangular hall has perimeter 250m. If the cost of painting the four walls

at the rate of RS.10 per m2 is Rs.15,000. Find the height of the hall.

316 Ajay has built a cubical water tank in his house. The top of the water tank is covered with

lid. He wants to cover the inner surface of the tank including the lid with square tiles of

side 25cm. If each inner edge of the water tank is 2m long and tiles cost Rs.360 per

dozen, then find the total amount required for tiles.

317 A cube and a cuboid have the same volume. The dimensions of the cuboid are in the

ration 1:2:4. If the difference between the cost of painting the cuboid and cube (whole

surface area) at the rate of Rs. 5/m2 is RS.80. Find their volumes.

318 The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of

the metal is 8.9 g per cm3 ?

319 Twenty seven solid iron spheres, each of radius r and surface area s are melted to form a

sphere with surface area s1. Find the

(i) Radius r1 of the new sphere

(ii) Ratio of s and s1

320 The volume of sphere is 38808 m3. Find its surface area.

321 A powder tin has square base with side 8 cm and height 13 cm. Another powder tin is

cylinder with base radius 7 cm and height 15cm. Which of two contains more powder ?

Also find the difference of their capacities.

322 Madhu has a piece of canvas, whose are is 550m2, He uses it to have a conical tent made,

with a base radius of 7m. Assuming the stitching wastage is negligible. Find the volume

of the tent that can be made with the canvas.

323 A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the

interiors. The radius of the cylindrical wood is 3.5 mm and the radius of the graphite is

0.5mm. If the length of the pencil is 14cm, find the volume of the wood (in cm3)

[use π =

]

324 Rain water which falls on a flat rectangular surface of length 6m and breadth 4m is

transferred into a cylindrical vessel of internal radius 20cm. What will be the height of

water in the cylindrical vessel if the rain fall is1cm. Give your answer to the nearest

whole number [use π=3.14]

325 A small indoor green house is made entirely of glass panes (including base) held together

with tape. It is 30cm long, 25cm wide and 25cm high. What is the area of the glass? How

much tape is required for all the 12 edges.

326 A hemispherical dome of a building needs to be painted. If the ear of the base is 24.64m2,

find the cost of painting it, given the cost of painting is Rs.5 per 100cm2. [Use π =

]

327 A Wall of length 10m was to be built across an open ground. The height of the wall is 4m

and thickness of the wall is 24cm. If this wall is to be built up with bricks whose

dimensions are 24cm x 12 cm x 8cm, how many bricks would be required?

328 A metal sheet 27cm long, 8cm broad and 1cm thick is melted into a cube. Find the

difference between surface areas of two solids.

329 The circumference of the base of a 16 m high solid cone is33m. Find the surface area of

the come [Use π =

]

(Statistics)

330 Draw a frequency polygon of the following data

Marks 30-40 40-50 50-60 60-70 70-80 80-90 90-100

No of students 11 7 9 20 22 2 3

331 Draw a histogram to represent the data.

Marks 0-20 20-60 60-80 80-100

No of students 5 20 16 8

(i) How many students got marks more than or equal to 60?

(ii) How many students got marks less than 20?

332 If mean of seven observations (taken in ascending order) 28, 32, x, x+2, x+5,43,45 is 38

find x and hence median.

333 In a city, the following weekly observations were made in a study on cost of living index.

Cost of living index 120-130 130-140 140-150 150-160 160-170 170-180

No of weeks 8 12 4 16 8 4

Draw a histogram and frequency polygon for above data.

334 Find the difference of mean and mode of the following data.

X 20 25 32 40 50 100

Y 5 4 10 2 1 3

335 Draw a histogram and frequency polygon of the following data.

Marks 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

No of

students

5 12 6 20 18 10 16 3

336 The daily earning of 30 works are given below :

Daily

earning

In

Rupees)

0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400

No of

workers 3 7 4 5 4 3 2 2

337 The distribution of weekly wages of 140 casual laborers in a factory is given below.

Draw a frequency polygon for the data.

Weekly

wages

210-230 230-250 250-270 270-290 290-310 310-330 330-350

No of

Laborers

4 7 5 9 5 6 4

338 Draw a histogram and frequency polygon for the following data:

CT 0-50 50-100 100-150 150-200 200-250 250-300

Frequency 12 18 27 20 17 6

339 Draw the histogram for the following data representing marks of students of a class in an

examination.

Marks

Obtained 0-10 10-20 20-30 30-50 50-80 80-90 90-100 100-120

No of

students 5 10 4 16 12 7 9 2

*-- *